For me, I would have transitioned regardless of society providing other options or not. When I was younger, I felt like my body did not reflect how I wanted to present myself to the world, so I presented something entirely different. No doubt that thought process was influenced by societal expectations placed on me.
As I got older, I embraced my masculine side more and more as I saw aspects of masculinity that I liked. However, my body dysphoria remained regardless of my acceptance of a more masculine gender role, so I doubt another option that allowed me to be present a less masculine side of me would have helped.
In fact, my ability to find happiness meeting western society's expectations of masculinity caused me more confusion and heartache than anything else. I honestly felt that I was not woman enough to transition, and that I had no business calling myself transsexual. I even thought I was fetishist , but I felt no sexual excitement while cross dressed.
When I finally decided to transition, both my family and therapist doubted my sincerity to transition because I wanted to maintain a more masculine personality. Thus the question became why transition when you are happy being masculine? To them, there really was no good reason for me to transition. My therapist seemed more than a little incredulous of my desire to transition, and would ask me on several occasions if I was happy as a woman.
Now that I think about it, if I had a third gender option when I was younger, I would probably be a lot more feminine today. If a third gender option became available during my adulthood, I would have transitioned sooner, and it would have probably been smoother.